Suppressed Ion-Scale Turbulence and Critical Density ...

Suppressed Ion-Scale Turbulence and Critical Density Gradient in the C-2

Field-Reversed Configuration L. Schmitz (UCLA, TAE)

with C. Lau, D. Fulton, I. Holod, Z. Lin, (UCI), !

T. Tajima, M. Binderbauer, H. Gota, B. Deng, J. Douglass (TAE) and the TAE Team!

!

!!

Norman Rostoker !Memorial Symposium!August 24-25, 2015!

Irvine, CA!!

5

0

-5

f D (

MH

z)

0 1 2Time (ms)

2 L. Schmitz Norman Rostoker

Memorial Symposium

Goal of FRC Turbulence/Transport Studies:�Active Profile, Boundary, and Transport Control

Transport Models,

Dimensionless Scaling

Predictive Kinetic

Turbulence Modeling

Advanced Turbulence/

Profile Measurements

Active Profile,

Boundary, Transport Control


Memorial Symposium

Outline § Introduction

§ Experimental fluctuation/turbulence studies in the C-2 FRC

§ Gyrokinetic Modeling: FRC core and boundary fluctuations

§ Critical gradients, core/SOL transition and barrier effects

§ Summary


Memorial Symposium

FRC Geometry / C-2 Parameters

Solenoid coil (External B-Field)

B-Field Null (R)

Separatrix (Rs) Scrape-off layer

Core Plasma

Bez

Typical C-2 Parameters

FRC Core SOL Density (1019 m-‐3)

2-‐4 0.5-‐2

Ti (eV) 600-‐1000 ≤250 Te (eV) ≤ 150 30-‐80 Be (Gauss) ≤ 1200 Sep. Radius (cm)

35-‐45

Neutral Beam Power

≤ 4 MW


Memorial Symposium

FRC Radial and Parallel Transport� Scrape-off layer (SOL):

Radial and parallel Transport (along z)

τ⊥−1 = 1

r∂∂r

rDr1n∂n∂r

⎛⎝⎜

⎞⎠⎟

Radial transport:

τ−1 = (τii lnRM )

−1

τ−1 = (τii lnRM )

−1

Radial Gradient scale length : If depends on , parallel and perpendicular transport are coupled

-10 -5 0 5 10

0.6

0.4

0.2

z (m)

r (

m)

From continuity (particle conservation:) ∇(nv i ) = −∇⊥ (nv i ) τ = τ⊥

Ln⊥

Ln⊥ = D⊥τ ii lnRM

D⊥

D⊥

Separatrix


Memorial Symposium

Schematic and Principle of Doppler Backscattering Diagnostic (DBS)

ts=ti-kevExBks=ki-ke

b

c

ke

kIkS

tI,kI

ee .Be,ez

ñ/n: local density fluctuation level ñ(r)/n(r) vs. kθ - here kθ~ 0.5-12 cm-1 (kθρs~1-40)

ExB velocity from Doppler shift of back-scattered signal: ωDoppler = vturb kθ ~ vExBkθ

è vExB ~ ωDoppler / 2ki


Memorial Symposium

Radial Density Profile and DBS Probing Radii

§  DBS: 6 remote-tunable channels (co-linear beams), probing the FRC core (outside field null) and the SOL

§  Beam path calculated via GENRAY ray/beam tracing, based on reconstructed (CO2) density profiles

ts=ti-kevExBks=ki-ke

b

c

ke

kIkS

tI,kI

ee .Be,ez

60

40

20

0

-20

-40

-60

-60 -40 -20 0 20 40 60

x (cm)

y (c

m)

750+s

MW Launch


Memorial Symposium

Density Fluctuations Peak Outside Separatrix Very Low Fluctuations in FRC Core

n  Fluctuation levels peak outside the separatrix n  Very low fluctuation levels in the FRC core

-20 -10 0 10 20rFIR < r6\(cm)

0.0

0.1

0.2

0.3

0.4

0.5

bn

/n

Doppler Backscattering FIR Scattering

2 <kρs < 8 kρs < 4

rr rFIR –Rs (cm)


Memorial Symposium

FRC Core Plasma: Unique Inverted Wavenumber Spectrum�

§  FRC Core: Decreased Fluctuations; Inverted Spectrum at low kρs

§  Spectrum extends to kρe > 0.3: Only unstable electron modes!

§  SOL: Ion and electron-scale modes

§  Broad exponential spectrum: (ñ/n)2 ~ exp (-0.32 kθρs)


Memorial Symposium





§ Summary


Memorial Symposium

GTC (Gyrokinetic Toroidal Code) Simulations

First-principles, integrated microturbulence simulations; adapted for FRC geometry (Boozer coordinates): Useful for predictive modeling and reduced transport models Input: Experimental (measured) or calculated FRC equilibria Gyrokinetic or kinetic ions, kinetic electrons Local/global simulations, electromagnetic effects Fokker-Planck-collisions Presented here: Results from linear, electrostatic flux-tube simulations, separate calculations for the FRC core and SOL Future work: Coupled SOL/core, kinetic ions, nonlinear runs


Memorial Symposium

Simulation Geometry, Parameters

Core and SOL local simulation: Realistic C-2 Equilibrium Periodic boundary conditions in z and θ Gyrokinetic ions (D) and electrons, νe,i*=ν/νtransit <<1


Memorial Symposium

FRC-Core: Ion Modes Suppressed via FLR Effects, only Electron Modes Unstable

Calculated Linear Growth Rate from GTC

Measured Saturated Spectrum

•  Spectrum extends to kθρe > 0.3: matches linearly unstable k-range Dominant electron modes; ion modes weak/absent due to FLR* effects:

*Rosenbluth, Krall and Rostoker, NF Suppl. pt1, 143 (1962)

kѡ��ѩe

0.8

0.4

��

aR/c

s 0.24 0.28 ��

d=1

Core

R/LTe=5.25

no collisions


Memorial Symposium

Ballooning Structure with/without Collisions

collisionless (ballooning) with collisions (ballooning, virtually no change in mode structure) θ

ζ

ζ

ζ


Memorial Symposium

Local Gyrokinetic SOL Simulations

i-‐i e-‐i e-‐e 0.0058 0.172 0.082

𝜈*

Gyrokinetic D Ions Drift-kinetic electrons Ti = 5Te, Zeff =1.5 Fokker-Planck Collisions Flux-tube, local �simulation at r/Rs=1.2; periodic boundary in z

⇒ 𝜈*e-‐e=𝜈e-‐e/(vth-‐e/L) (moderate electron collisionality )

SOL


Memorial Symposium

SOL: Exponential Wavenumber Spectrum;Unstable Ion Modes

#29587-29610, #29750-29802

ρs=[(kTe+kTi)/mi]1/2/ωci

Measured Saturated Spectrum Calculated Linear Growth Rate from GTC (w/collisions)


Memorial Symposium

Driving Gradients Differ in FRC Core and SOL aR

/cs

3.0

2.0

1.0

00.75 0.8 0.85 0.9 0.95 1.0

de

Core di=1

R/LTi=R/Ln= 6

no collisions

kѡ� ѩe=0.3

∇Te ∇n

No instability below ηe <0.75

Electron drift/Interchange Core modes driven by and curvature

Instability to 1/ηi =0

Density gradient-driven SOL ion drift modes

aR/c

s

0.3

0.2

0.1

00 0.2 0.4 0.6 0.8 1.0

� di

R/LTe= R/LTi

= 6

SOL�de=1

kels= 0.85

w/collisions

SOL Modes are Driven by Core Modes are Driven by

∇Te


Memorial Symposium





§ Summary


Memorial Symposium

E×B Shear Increases the SOL Critical Gradient

§  Radial density gradient increases after ~0.5 ms (SOL is depleted) §  SOL fluctuation increase once critical density gradient is exceeded §  Fluctuation decrease once ExB shearing rate increases exceeds the turbulence decorrelation rate: ωΕ×Β>ΔωD (Biglari, Diamond, Terry, Phys. Fluids B1,1989) §  The radial correlation length decreases with increasing ExB shear

Density profile time history

6

4

2

0

R/L n

0.14

0.07

0

0 0.5 1.0 1.5 2.0 2.5

1.0

0.5

0

-0.5

Time (ms)

t E�B

, tD (

106 ra

d/s)

ñ/n (a

u)1.5

1.0

0.5

0

h r (c

m)

R/Ln crit

0.6

0.4

0.2

0

0.2

0.4

0.6

r (m

)

2.3

1.9

1.5

1.1

0.7

0.4

0

ne (1019 m-3)

r/Rs=1.1

r/Rs=1.1

r/Rs=0.9

r/Rs=0.9


Memorial Symposium

Measured Critical Gradient and Calculated Core Linear Threshold from GTC

a R/

c s

2.0

1.5

1.0

0.5

0

R/LTe, R/Ln4.8 5.2 5.6

r/Rs=0.97 Corekele = 0.27kele = 0.30

de= di= 1

2 3 4R/Ln

0.16

0.08

0

ñ/n

(au)

r/Rs ~ 1.15r/Rs = 0.95r/Rs ~ 0.85

kele ~ 0.07-0.28

R/Ln critR/Ln crit

(SOL)(Core)

Measured R/ Ln crit (FRC core/SOL)

FRC core growth rate vs. R/LTe from linear GTC simulation


Memorial Symposium

2 3 4R/Ln

0.16

0.08

0

ñ/n

(au)

r/Rs ~ 1.15r/Rs = 0.95r/Rs ~ 0.85

kele ~ 0.07-0.28

R/Ln critR/Ln crit

(SOL)(Core)

R/Ln

kels = 0.85kels = 1.70

3 4 5 6

0.4

0.3

0.2

0.1

0a R

/cs

R/Ln

r/Rs=1.2 SOL

kels = 0.85kels = 1.70

3 4 5 6

Measured SOL Critical Density Gradient Similar to Predicted Linear Instability Threshold

Measured R/ Ln crit (FRC core/SOL)

FRC core growth rate vs. R/Ln from linear GTC simulation


Memorial Symposium

Core-SOL Coupling: Evidence �for Radial Transport Barrier

§  Radial turbulence correlation

length λr ≤ ρi §  No evidence of sustained extended radial structures or streamers λr reduced just outside Rs: Evidence of radial transport barrier. §  Shear decorrelation just outside the separatrix: ωΕ×Β>ΔωD (Biglari, Diamond, Terry,

Phys. Fluids B1,1989)

-10 0 10

tE

xB, 6

tD

(1

05 r

ad/s

)

r-Rs (cm)

6

4

2

0

>


Memorial Symposium

Summary •  C-2 FRC core: Ion modes stable due to FLR effect; only

electron modes unstable (driven by electron temperature gradient and curvature)

•  Moderate, larger-scale ion-mode SOL turbulence observed/predicted; driven by the radial density gradient.

•  Strong evidence of radial transport barrier in the SOL. No experimental evidence of sustained large-scale radial structures/streamers (radial correlation length λr < ρi)

•  Observed critical SOL density gradient compares well

with predicted linear instability threshold; compatible with required reactor SOL width

Thank you for your attention!

Suppressed Ion-Scale Turbulence and Critical Density ...

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